I've been trying to pick up Piper's perk because it seems like one that would benefit me the most right now (I've got a lot of undiscovered locations), but I'm not sure how it pops up. She's opened up to me about her dad, nothing further though.
Weird, I thought the perk unlocks for all time. So you don't need that npc anymore. Not really had much call to test it though.
Once you reach max affinity, there will be a message that tells you the name of the perk. But you have to find it in the Pipboy to see the effects.
And you don't need to romance them to get the perk. As for romance itself, there isn't anything gratuitous or sixy about it. If you sleep in a bed with them nearby you'll get the Lover's Embrace bonus instead of Well Rested (works on any bed though), and they'll say something cute as they crawl out of bed. That's about it.